Men's free skate score standard deviation

This might just be interesting for math geeks, but nere it is nonetheless. Standard deviation is basically how much a set of numbers diverges. This is relevant for FS scores because a small standard deviation means all judges pretty much agree whereas a large deviation means there is no agreement. For example, scores of 7.25,7.5,7.5, 7.75 have standard deviation of 0.2, whereas scores 6.5, 7.25, 7.75, 8.5 have s.d. of 0.84. Mathman, feel free to explain it better

I thought it would be interesting to see standard deviations in the component scores of men free skate. Note that I took a standard deviation for all components and all judges, so I had a set of 40 numbers for each skater (5 components times 8 judges). In general, standard deviation grows as we move down the ranks, that makes sense. What I found interesting, though, was that by far the largest standard deviation of the night went to Plushenko (Lysacek's is among the smallest). Also found it interesting that Weir's deviation wasn't all that big at all (I thought it was a matter of just some judges not liking him - not so).

So, here it is, in order from largest deviation to the smallest; number in parenthesis indicates placement for the free skate.

This might just be interesting for math geeks, but nere it is nonetheless. Standard deviation is basically how much a set of numbers diverges. This is relevant for FS scores because a small standard deviation means all judges pretty much agree whereas a large deviation means there is no agreement. For example, scores of 7.25,7.5,7.5, 7.75 have standard deviation of 0.2, whereas scores 6.5, 7.25, 7.75, 8.5 have s.d. of 0.84. Mathman, feel free to explain it better

I thought it would be interesting to see standard deviations in the component scores of men free skate. Note that I took a standard deviation for all components and all judges, so I had a set of 40 numbers for each skater (5 components times 8 judges). In general, standard deviation grows as we move down the ranks, that makes sense. What I found interesting, though, was that by far the largest standard deviation of the night went to Plushenko (Lysacek's is among the smallest). Also found it interesting that Weir's deviation wasn't all that big at all (I thought it was a matter of just some judges not liking him - not so).

So, here it is, in order from largest deviation to the smallest; number in parenthesis indicates placement for the free skate.

Plushenko (2) - 0.8953

Ten (14) - 0.8581

Kovalevsky (24) - 0.7530

Pfeifer (20) - 0.7426

Bacchini (22) - 0.7150

Lindemann (23) - 0.6920

Borodulin (12) - 0.6880

Chipeur (21) - 0.6810

Verner (17) - 0.6752

Joubert (16) - 0.6691

van der Perren (18) - 0.6613

Schultheiss (13) - 0.6579

Contesti (19) - 0.6373

Fernandez (10) - 0.5901

Weir (6) - 0.5568

Lambiel (3) - 0.5367

Brezina (11) - 0.5282

Kozuka (8) - 0.5171

Oda (7) - 0.5144

Abbott (9) - 0.5042

Lysacek (1) - 0.4413

Chan (4) - 0.4367

Takahashi (5) - 0.42957

Amodio (15) - 0.4291

HA! Plushenko first....some love him, some hate! Happy to see most agreed with Lysacek, Weir, and Takahashi's placement.

This might just be interesting for math geeks, but nere it is nonetheless. Standard deviation is basically how much a set of numbers diverges. This is relevant for FS scores because a small standard deviation means all judges pretty much agree whereas a large deviation means there is no agreement. For example, scores of 7.25,7.5,7.5, 7.75 have standard deviation of 0.2, whereas scores 6.5, 7.25, 7.75, 8.5 have s.d. of 0.84. Mathman, feel free to explain it better

I thought it would be interesting to see standard deviations in the component scores of men free skate. Note that I took a standard deviation for all components and all judges, so I had a set of 40 numbers for each skater (5 components times 8 judges). In general, standard deviation grows as we move down the ranks, that makes sense. What I found interesting, though, was that by far the largest standard deviation of the night went to Plushenko (Lysacek's is among the smallest). Also found it interesting that Weir's deviation wasn't all that big at all (I thought it was a matter of just some judges not liking him - not so).

Or do an SD of SP, LP scores in the past few competition
Plushenko is closer to 0.
Lysacek is closer to 1. Lysacek magically got 90 in the SP and 167 in the LP. His SD deviated too much from normal score. Plushenko, on the other hand, doesn't.

It's how you play with number and present them. So take with a grain of salt. =).

I think the main reason for Plushenko's large standard deviation is not so much the differences among the judges but rather the differences from one component to the next, across all judges.

For instance, both Plushanko's and Lysacek's marks were lowest in Transitions and highest in Performance/Execution. But the spread between the two was 1.50 for Plushenko (7.25 to 8.80 -- the Joe Inman effect ) and only 0.55 (7.95 to 8.50) for Lysacek.

One could do a two-way analysis of variance (ANOVA) and split out the part of the standard deviation due to differences among the judges and the part due to differences among the components.

Ptitcka, can you give a link to the scores for the individual judges? On the ISU and Olympic Games sites I could only find summaries.

That's really illuminating. Interesting that Patrick is also among those with the least divergence..

Illuminated one thing: judges got a memo to be supremely generous to hometown boy.
Patrick Chan scored a personal best for THAT LP. It would be shocking if his wasn't among those with the least divergence.

This might just be interesting for math geeks, but nere it is nonetheless. Standard deviation is basically how much a set of numbers diverges. This is relevant for FS scores because a small standard deviation means all judges pretty much agree whereas a large deviation means there is no agreement. For example, scores of 7.25,7.5,7.5, 7.75 have standard deviation of 0.2, whereas scores 6.5, 7.25, 7.75, 8.5 have s.d. of 0.84. Mathman, feel free to explain it better

I thought it would be interesting to see standard deviations in the component scores of men free skate. Note that I took a standard deviation for all components and all judges, so I had a set of 40 numbers for each skater (5 components times 8 judges). In general, standard deviation grows as we move down the ranks, that makes sense. What I found interesting, though, was that by far the largest standard deviation of the night went to Plushenko (Lysacek's is among the smallest). Also found it interesting that Weir's deviation wasn't all that big at all (I thought it was a matter of just some judges not liking him - not so).

So, here it is, in order from largest deviation to the smallest; number in parenthesis indicates placement for the free skate.

Plushenko (2) - 0.8953

Ten (14) - 0.8581

Kovalevsky (24) - 0.7530

Pfeifer (20) - 0.7426

Bacchini (22) - 0.7150

Lindemann (23) - 0.6920

Borodulin (12) - 0.6880

Chipeur (21) - 0.6810

Verner (17) - 0.6752

Joubert (16) - 0.6691

van der Perren (18) - 0.6613

Schultheiss (13) - 0.6579

Contesti (19) - 0.6373

Fernandez (10) - 0.5901

Weir (6) - 0.5568

Lambiel (3) - 0.5367

Brezina (11) - 0.5282

Kozuka (8) - 0.5171

Oda (7) - 0.5144

Abbott (9) - 0.5042

Lysacek (1) - 0.4413

Chan (4) - 0.4367

Takahashi (5) - 0.42957

Amodio (15) - 0.4291

Ptichka, first thank you for the effort. I think there is flaw in this analysis. Your analysis is based on an assumption that a skater is even in all 5 elements of the PCS, so you suppose that they should be all in line with each other. But it is not the case. For example, Plushenko's transition is much lower than the other four, and performance was high compared to the other three if I remember it correctly. That might explain why he's among the highest in SD. So it might make more sense to do it by each element (SS, TR, ect). In my opinion it is right to have different means for different element as ,for example, a skater could get different choreography/composition and transition scores according different program, but his SS and the other should not change that much. Just a suggestion.

In fact, I now did a spread for all components AND averages for GoE deviations. Table here: http://ptichkafs.livejournal.com/46416.html
Not only is Plush's component standard deviation very high (though calculated this way, it's not THE highest - that honor goes to Ten), but the average of standard deviations for each of the GoE's is the highest at 0.7560 (though Takahashi's at 0.7522 is about the same) - the norm is far lower.